find breaking the numbers down to their prime factors ∛512
512 = 8^3 = 2^9
http://www.easycalculation.com/cube-roots-512.html
To find the prime factors of a number, we can start by taking the cube root of the number. In this case, we want to find the cube root of 512.
The cube root of a number can be calculated by finding the number that, when multiplied by itself three times, gives the original number. In other words, if we have a number x and its cube root is y, then y * y * y = x.
To find the cube root of 512, we can use a calculator or approximate it manually. In this case, the cube root of 512 is approximately 8.
Now that we have the cube root, we can start breaking down the number into its prime factors. The prime factors are the prime numbers that multiply together to create the original number.
To find the prime factors, we divide the number by the smallest prime number, which is 2. If the number is divisible by 2, we divide it until it is no longer divisible by 2. In this case, 512 is divisible by 2, so we divide 512 by 2 repeatedly until we can no longer divide it evenly.
512 ÷ 2 = 256
256 ÷ 2 = 128
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8 ----------> This is the cube root we found earlier.
Now that we have a value of 8, which is the cube root of 512, we know that 512 can be broken down into three factors of 8.
Therefore, the prime factorization of 512 can be written as:
512 = 8 * 8 * 8
Alternatively, we can write it using exponents:
512 = 2^9
So, the prime factorization of ∛512 is 2^9, where '^' represents the exponentiation symbol.